Finite Group Databasebeta

← #14290931

Subgroups — #14290931

Order 1920.

460 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5700C211yesmaximal, characteristic, complemented
2#11751168C211yesmaximal, characteristic, complemented
3#11747032C212yesmaximal, complemented
4C3×#64763C211yesmaximal, characteristic, complemented
5#11745847C212yesmaximal, complemented
6#10602745—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91763C2211yescharacteristic
9C5×#896—22no—
10C5×#895—22no—
11C5×#894—22no—
12C5×#875C2212yes—
13C2×#6660—22no—
14C2×#6654—22no—
15#91093—22no—
16#91087C2211yescharacteristic
17C3×#3935C2212yes—
18#68370—51nomaximal, Hall
19C5×#562—31no—
20#65356—31no—
21#65347—32no—
22#64763D311yescharacteristic, complemented
23#64760—32no—
24C2×D60—22no—
25C2×D60—21no—
26C2×C5×D12—22no—
27C2×C5×D12D412yes—
28C2×C4×C5×D3—22no—
29C2×C5×Dic6D412yes—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C42×C5C2311yescharacteristic
33C2×C3⋊#168—21no—
34C5×(C2×D3)⋊C4—22no—
35C5×(C2×D3)⋊C4—22no—
36C5×(C2×D3)⋊C4—22no—
37C5×Dic3⋊C4—22no—
38C2×C3×#168—22no—
39#6660—44no—
40#6654—44no—
41#5700D511yescharacteristic, complemented
42#5067—51no—
43#4712—52no—
44C3×#330—51no—
45#4464—52no—
46C5×#125C2×D311yescharacteristic
47C5×#124—32no—
48C5×#123—62no—
49C5×C22⋊Q8—62no—
50C5×#121—62no—
51C2×#688—62no—
52C2×#686—62no—
53#4020—31no—
54#3941—62no—
55#3935—31no—
56#3935C2×D312yes—
57#1656—151noSylow
58C22×D15—41no—
59C22×C5×D3—22no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63D60—42no—
64D60—42no—
65D60—42no—
66C2×C5×Dic3—22no—
67C5×D12—42no—
68C5×D12—82no—
69C4×C5×D3—82no—
70C5×Dic6—42no—
71C3⋊#168—41no—
72C3×#168—24no—
73C3×#125C2×D511yescharacteristic
74C2×D24—102no—
75C2×#204—102no—
76#896—22no—
77#895—22no—
78#894—22no—
79#875C2×D512yes—
80#874—51no—
81C3×#97—52no—
82#809—102no—
83#803—51no—
84C2×C5×Q8—32no—
85C2×C5×D4—32no—
86C2×C5×D4—62no—
87C22×C4×C5—62no—
88C2×D20—61no—
89C2×D20—62no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4—62no—
92C5×C4⋊C4D1212yes—
93C5×C22⋊C4—62no—
94C5×C22⋊C4—62no—
95C5×C22⋊C4—62no—
96C42×C5C22×D311yescharacteristic
97#688—124no—
98#686—124no—
99C2×#168—22no—
100C2×#168—61no—
101#562—31no—
102#496—152no—
103#490—151no—
104#330—51no—
105#329—152no—
106C22×C3×C5#12011yescharacteristic
107C2×D15—82no—
108C2×D15—81no—
109C2×C5×D3—42no—
110C2×C5×D3—42no—
111C2×C5×D3—42no—
112C3×C4×C5—22no—
113C3×C4×C5—21no—
114C3×C4×C5—42no—
115C5×Dic3—42no—
116C2×D12—22no—
117C2×D12—101no—
118C2×D12—102no—
119C2×D12C22⋊D512yes—
120C2×C4×D3—22no—
121C2×Dic6C22⋊D512yes—
122C2×C3×C8—102no—
123C3×C4⋊C4—22no—
124C3×C4⋊C4C22⋊D512yes—
125C3×C42C22×D511yescharacteristic
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129Dic3⋊C4—22no—
130C2×C3⋊C8—101no—
131D24—204no—
132#204—204no—
133C23×C5—62no—
134C22×D5—121no—
135C5×Q8—122no—
136C5×D4—122no—
137C5×D4—242no—
138C2×C4×C5—22no—
139C2×C4×C5—62no—
140C2×C4×C5—242no—
141C2×C4×C5C2×D1211yescharacteristic
142C2×C4×C5D3×D412yes—
143D20—122no—
144D20—122no—
145D20—122no—
146#168—24no—
147#168—121no—
148C2×SD16—302no—
149C2×D8—302no—
150#127—151no—
151#125D3×D511yescharacteristic
152#124—32no—
153#123—62no—
154C22⋊Q8—62no—
155#121—62no—
156#102—302no—
157#97—52no—
158#97—151no—
159C2×C3×C5#45312yes—
160C2×C3×C5#45411yescharacteristic
161D15—161no—
162C5×D3—82no—
163C22×D3—22no—
164C22×D3—201no—
165C2×C3×C4—22no—
166C2×C3×C4C2×C22⋊D511yescharacteristic
167C2×C3×C4C2×C22⋊D512yes—
168C2×Dic3—22no—
169D12—42no—
170D12—82no—
171D12—202no—
172D12—202no—
173D12—202no—
174C4×D3—82no—
175Dic6—42no—
176C3×C8—104no—
177C3⋊C8—201no—
178C22×C5—122no—
179C22×C5—122no—
180C22×C5—122no—
181C22×C5#88211yescharacteristic
182C2×D5—241no—
183C2×D5—242no—
184C4×C5—21no—
185C4×C5—22no—
186C4×C5—42no—
187C4×C5—122no—
188C2×Q8—32no—
189C2×D4—32no—
190C2×D4—62no—
191C2×D4—301no—
192C2×D4—302no—
193C22×C4—62no—
194SD16—604no—
195D8—604no—
196C2×C8—102no—
197C2×C8—301no—
198C4⋊C4—22no—
199C4⋊C4—62no—
200C4⋊C4#120312yes—
201C22⋊C4—62no—
202C22⋊C4—62no—
203C22⋊C4—62no—
204C42C2×D3×D511yescharacteristic
205C3×C5#165611yescharacteristic, complemented, Hall
206C22×C3#409911yescharacteristic
207C2×D3—42no—
208C2×D3—42no—
209C2×D3—42no—
210C2×D3—402no—
211C2×D3—401no—
212C3×C4—22no—
213C3×C4—21no—
214C3×C4—42no—
215Dic3—42no—
216C2×C5—242no—
217C2×C5#475311yescharacteristic
218C2×C5#482212yes—
219D5—481no—
220C23—62no—
221C23—601no—
222Q8—122no—
223D4—122no—
224D4—242no—
225D4—602no—
226D4—602no—
227D4—602no—
228C2×C4—22no—
229C2×C4—62no—
230C2×C4—242no—
231C2×C4C2×#120311yescharacteristic
232C2×C4D3×C22⋊D512yes—
233C8—104no—
234C8—601no—
235C2×C3#6553012yes—
236C2×C3#6553411yescharacteristic
237D3—82no—
238D3—801no—
239C5#6837011yescharacteristic, complemented, Sylow
240C22—122no—
241C22—122no—
242C22—122no—
243C22—1201no—
244C22—1202no—
245C22#9157011yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4—122no—
250C3#1060274511yescharacteristic, complemented, Sylow
251C2—242no—
252C2—2401no—
253C2#1174938711yescharacteristic
254C2#1174942012yes—
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
hypercenter#125D3×D5
hypocenterC3×C5#1656
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×#5700C2semidirect
2. #11751168C2semidirect
3. #11747032C2semidirect
4. C3×#64763C2semidirect
5. #11745847C2semidirect
22. #64763D3semidirect
41. #5700D5semidirect
205. C3×C5#1656semidirect
239. C5#68370semidirect
250. C3#10602745semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×#57002
#117511682
#117470322
C3×#647632
#117458472
#106027453
#683705